Hybrid-illumination Multiplexed Fourier Ptychographic Microscopy (HMFPM)

This repository contains the implementation and demonstration datasets for the paper:

Hybrid-illumination multiplexed Fourier ptychographic microscopy with robust aberration correction

arXiv: https://arxiv.org/abs/2509.05549

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Table of Contents

• Introduction
• Repository Structure
• Installation
• Usage
• Example Results
• BiBTeX

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Introduction

Hybrid-illumination Multiplexed Fourier Ptychographic Microscopy (HMFPM) is an advanced computational imaging framework that integrates the advantages of multiplexed FPM and Analytic Pupil function with Incoherent Contrast (APIC) methods.

The workflow consists of two stages:

1. Bright-field initialization

   • Acquire eight NA-matched measurements.
   • Apply Kramers–Kronig (K–K) relations and analytic aberration extraction to reconstruct the bright-field spectrum.
   • Estimate the pupil function analytically.

2. Dark-field multiplexed reconstruction

   • Record a small number of dark-field measurements with 3–6 simultaneously illuminated LEDs in specially designed multiplexing patterns.
   • Use a customized optimization algorithm to reconstruct the dark-field spectrum, initialized and constrained by the aberration-corrected bright-field spectrum and the extracted pupil function.

(1) Experimental setup and illumination strategy for HMFPM	(2) Reconstruction pipeline for HMFPM

Advantages over MFPM and APIC:

• Significantly reduces the number of required measurements.
• Provides robust aberration correction.
• Ensures fast and stable convergence without tuning relaxation factors.

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Repository Structure

├── Data                               # Raw simulation and experimental datasets
├── HMFPM_experiment.py                # Main pipeline for experimental data
├── HMFPM_simulation.py                # Main pipeline for simulation data
├── subfunctionAPIC                    # Subfunctions for HMFPM reconstruction
└── README.md                          # Project documentation

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Installation

1. Clone this repository to your local machine:

   git clone https://github.com/Magishe/HMFPM.git

2. Navigate to the project directory:

   cd HMFPM

3. Install the dependencies: To set up your environment and install all the necessary packages, run the following command:

   pip3 install torch==2.1.1+cu121 torchvision==0.16.1+cu121 torch-dct==0.1.6 --index-url https://download.pytorch.org/whl/cu121
   pip3 install numpy scipy matplotlib pillow h5py opencv-python

Usage

1. Using the demo data

    python HMFPM_experiment.py
    python HMFPM_simulation.py

2. Construct your own data

To run HMFPM on your own data, you need to create a MATLAB v7.3 .mat file that contains the required experimental parameters and raw measurements. Save this file under the path:

Data/experiment/

Required variables in the .mat file

• dpix_c: Camera pixel size in micrometers (e.g., 3.45 µm).

• lambda_g: Illumination wavelength in micrometers (e.g., 0.520 µm).

• mag: Objective magnification (e.g., 4).

• na_illu: Illumination numerical aperture of the NA-matching illumination (e.g., 0.1254).

• na_obj: Objective numerical aperture (e.g., 0.1310).

• na_rp_cal: Calibrated spatial frequency coordinates of system NA.

• freqXY_calib_BF (double, N×2) Calibrated spatial frequency coordinates for NA-matching LEDs.
  It is calculated as:

  freqXY_calib = (patch_size * dpix_c) / (mag * lambda_g) * illumination_NA + [patch_size/2, patch_size/2]

• freqXY_calib_DF (cell, 1×N_D)
  Calibrated spatial frequency coordinates for dark-field LEDs. Here, N_D denotes the total number of dark-field measurements. Each cell stores a 2D freqXY_calib coordinate, corresponding to the set of LEDs that are illuminated simultaneously in one measurement. These coordinates are calculated using the same equation as for freqXY_calib_BF.

• I_low (uint16, H×W×(N+N_D))
  Raw low-resolution intensity stack, where H and W are the image dimensions (e.g., 2048×2048), N is the number of NA-matching measurements, and N_D is the number of multiplexed dark-field measurements. The first N frames correspond to NA-matching measurements, followed by N_D frames corresponding to multiplexed dark-field measurements.

Example results

Simulation results

(1) Siemens star simulation	(2) Natural image simulation

Experimental results

(1) Siemens star experiments	(2) NSCLC phase sample experiments

BiBTeX

@misc{zhao2025hybridilluminationmultiplexedfourierptychographic, title={Hybrid-illumination multiplexed Fourier ptychographic microscopy with robust aberration correction}, author={Shi Zhao and Haowen Zhou and Changhuei Yang}, year={2025}, eprint={2509.05549}, archivePrefix={arXiv}, primaryClass={physics.optics}, url={https://arxiv.org/abs/2509.05549}, }